Question

The area of the triangle formed by the tangent at the point $(a,b)$ to the circle $x^2+y^2=r^2$ and the coordinate axes is

• A. $\frac{r^4}{2ab}$
• B. $\frac{r^4}{3|ab|}$
• C. $\frac{r^4}{ab}$
• D. $\frac{r^4}{|ab|}$

Answer 1

The correct option is A $\frac{r^4}{2ab}$

Equation of tangent will be given by $T=0$
$ax+by=r^2$
hence the x intercept is $\frac{r^2}{a}$
and y intercept is $\frac{r^2}{b}$
so area of triangle is $\frac{1}{2}\frac{r^2}{a}\times \frac{r^2}{b}=\frac{r^4}{2ab}$